The two circles w

Given, Two Circles with Centers X and Y intersect each other at point A and B. S is a mid-point of XY, AS is perpendicular to PQ.

To Prove: AP = AQ

Construction: XM perpendicular to chord PA. And YN perpendicular to chord AQ of respective circles.

Since SA is also perpendicular to PQ (given)

So, all these perpendiculars to the same line are parallel to each other.

SX = SY

AM = AN

So,

AP = AQ